Unlike monogenic diseases whose genetic determinants have been mapped in extended human pedigrees using classical penetrance-based linkage analysis methods, many common diseases involve multiple genetic and environmental components and their interactions. The genetic analysis of such complex phenotypes requires new statistical approaches for the localization and evaluation of the relative importance of specific quantitative trait loci (QTLs). In this application, the investigators propose to develop/extend a number of new statistical genetic analytical methods for the localization and evaluation of QTLs influencing common human diseases. To address this critical area of genetic research, they have formed a new collaborative scientific team combining two major statistical genetic working groups based at the Southwest Foundation for Medical Research (led by Dr. Blangero) and the University of California at Los Angeles (led by Dr. Lange). Unlike most work in this nascent field, they will concentrate their efforts on methods for the analysis of common diseases and other complex phenotypes in extended human pedigrees. In particular, they will focus largely on extensions of the variance component method of linkage analysis. They will also further develop and extend their linkage analysis software (SOLAR) so that it becomes a comprehensive, yet easily used, package for the oligogenic analysis of quantitative human variation. The proposed research will address five specific aims: 1) The investigators will develop and extend the variance component linkage procedures to allow for general multivariate analysis, oligogenic inheritance, epistasis, genotype x environment interaction, and empirical genome-wide p-value evaluations; 2) They will develop more efficient methods for the calculation of IBD probability matrices in complex pedigrees; 3) A general variance component method for the linkage analysis of discrete traits and the joint analysis of discrete and quantitative traits will be formulated, tested, and implemented in the SOLAR package; 4) Two new methods for fine mapping QTLs in extended pedigrees will be developed and evaluated including joint disequilibrium/linkage analysis using variance component model and a novel gamete competition model; and 5) All of the above methods will be incorporated into the software package (SOLAR) for linkage analysis of complex traits in extended pedigrees.